Bottom antireflective coatings (B.A.R.C.'s) are used in microlithography to reduce the effects of the periodic variation of photoresist sensitivity with film thickness (the so-called swing curve) and to remove or reduce the effect of reflections off non-planar substrates. A well-known phenomenon is the dimensional variation of lines going over steps: reflection of light by the non-vertical sidewalls of the step causes increased incoupling of energy into the resist volume adjacent to the step, leading to a reduction in linewidth ("reflective notching"). Similar effects may be observed on reflective materials with a particularly coarse-grained structure.
It has been shown in the literature (T. Brunner, Proc. SPIE 1466, 297 (1991)) that the amplitude of the swing curve, defined as the so-called "swing ratio" S, may be approximated by EQU S=4(R.sub.t R.sub.b).sup.1/2 exp(-.alpha. d) (1)
where R.sub.t is the reflectance at the top of the resist layer, e.g. to air or to a top antireflective layer, R.sub.b is the one at the bottom, e.g., to the substrate or to a bottom antireflective layer, and d is the resist film thickness.
In the following, we will be writing the resist refractive index as a complex number N.sub.r =n.sub.r -ik.sub.r, where n.sub.r is the real part of N.sub.r, and is equivalent to what is commonly called "the refractive index", k.sub.r, the imaginary part of N.sub.r, is often referred to as the extinction coefficient. It is related to the absorption coefficient as a function of wavelength, .alpha..sub.r (.lambda.), by k.sub.r =.alpha..sub.r .lambda./(4.pi.).
the substrate/bottom coat/resist/air film stack can in good approximation be treated as a three layer system in which a thin bottom antireflective cost is sandwiched between semi-infinite resist and substrate layers. In this case, the amplitude of reflection off the BARC is given by EQU .rho..sub.b -(.rho..sub.rb +.rho..sub.bs .pi..sup.2)/(1+.rho..sub.rb .rho..sub.bs .pi..sup.2), (2)
where .rho..sub.rb =(N.sub.r -N.sub.b)/(N.sub.r +N.sub.b), .rho..sub.bs =(N.sub.b -N.sub.b)/N.sub.b +N.sub.s) are reflection coefficients, .pi..sup.2 =exp(-i 4.pi./.lambda.N.sub.b t) is the phase factor, t is the bottom antireflector film thickness, and the subscripts r,b, and s denote resist, bottom coat, and substrate, respectively. For absorbing films, .rho..sub.b is a complex number. The reflectance off the bottom coat is given by R=.rho..sub.b .rho..sub.b *, where the star denotes taking the complex conjugate.
It follows from the above that, very much like a photoresists, bottom antireflective coatings are subject to interference effects which cause a periodic variation in the intensity of the reflected light with increasing thickness of the layer. Since a bottom ARC is much more absorbing than a photoresist, the bottom ARC "swing curve" is, however, severely damped. All reflection transmission factors and the phase coefficient are complex numbers. The calculation therefore quickly becomes rather messy and yields quite cumbersome expressions; we have chosen to carry it out with the symbolic algebra package of the Mathematical program (copyright Wolfram Technologies, Inc.), or with a Microsoft.RTM. Excel.TM. spreadsheet written using the complex number handling provided by the Excel.TM. analysis toolpack. When interpreting the reflectance values of FIG. 1, it should be kept in mind that the swing ratios are proportional to the square root of the reflectance, not to the reflectance itself.
Analysis results indicate that for low values of the bottom coat extinction coefficient k.sub.b, the reflectance does not reach near-zero values in the first interference minima; however, it reaches very low values for very thick bottom coats. In contrast, for high k.sub.b, the first minimum already comes close to zero reflectance, but the reflectance for thicker films is so high that subsequent minima have higher reflectance, and the asymptotic reflectance for very thick films is much higher. Basically, this means that very absorbing thick bottom coats start to act as mirror elements of their own; essentially in the same way that metals are good mirrors precisely because they are so highly absorbing.
By considering the continuity conditions for the electric and magnetic field amplitudes in Maxwell's equations at the boundaries of semi-infinite resist and bottom coat layers, it is possible to derive an equation for the reflectance at infinite film thickness: ##EQU1## where the subscript r denotes the refractive index components of the resist, and b those of the bottom coat. As can be easily ascertained by inserting typical values of resist and bottom coat real and imaginary refractive indices, for practically encountered values of the optical constants the major contribution to the reflectance at infinite film thickness comes from the mismatch in the imaginary parts, not the real parts. Since a bottom coat needs to be absorbing, this mismatch in the imaginary parts is unavoidable and inherent in the concept of a bottom coat. In a nutshell, the above treatment therefore indicates that for every intended film thickness, there is an optimum extinction. Thin antireflective layers will have to be very absorbing, while thick layers should be designed with lower absorptivities.
For the real part of the refractive index, eq. (3) thus indicates that, for high values of the BARC film thickness, the reflectivity is minimal in the case of a perfect match of resist and bottom coat refractive indices (n.sub.r =n.sub.b). This is confirmed by a contour plot of the reflectivity R at the resist/bottom coat interface vs n.sub.b and the bottom coat thickness t (FIG. 1). A resist refractive index of n.sub.r =1.7 was used in the calculation; other optical parameters were: k.sub.r =0.04, k.sub.b =0.334, n.sub.s =5.0, k.sub.s =0.25, .lambda.=365 nm (exposure wavelength). For the commonly used diazonaphthoquinone/novolak g- and i-line materials frequently encountered values of n.sub.r are 1.64 to 1.69 at 435 nm, and 1.66 to 1.72 at 365 nm.
It is seen by inspection of FIG. 1 that the minima are lined up along the n.sub.r =1.7 line for larger B.A.R.C. thicknesses. For smaller film thicknesses, especially for the region of the first interference minimum, it would be advantageous to have lower resist refractive indices. It is, however, possible to choose a B.A.R.C. refractive index which works well at both thin and thick B.A.R.C. films. One such possible line has been drawn in FIG. 1 at n.sub.b =1.653.
It has been shown above that the optimum B.A.R.C. refractive index for higher film thickness is equal to the resist refractive index, and that for lower thicknesses, it is possible to find workable compromises which allow one to use a B.A.R.C. with a refractive index slightly lower than the resist refractive index for both low and high film thicknesses. What has not been shown is how to achieve the index match condition. This will be shown in this invention.